Molecular Atomic Clock With Wave Propagating Rotational Spectroscopy Cell

ABSTRACT

In an example, an apparatus comprises a sealed container containing a dipolar gas. The apparatus also comprises a first transmit antenna, a second transmit antenna, and a receive antenna each communicatively coupled to the sealed container. The apparatus also comprises a control circuit including a transceiver, the control circuit having a first transmit output, a second transmit output, and a receive input, the first transmit output coupled to the first transmit antenna, the second transmit output coupled to the second transmit antenna, and the receive input coupled to the receive antenna.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No. 17/001,356, filed Aug. 24, 2020, which is a continuation of U.S. patent application Ser. No. 16/234,492 filed Dec. 27, 2018, now U.S. Pat. No. 10,754,302, granted on Aug. 25, 2020, which claims priority to U.S. Provisional Patent Application No. 62/612,074 filed Dec. 29, 2017, all of which are hereby fully incorporated herein by reference for all purposes.

This application is related to co-pending co-assigned U.S. patent application Ser. No. 16/871,835 filed May 11, 2020.

BACKGROUND

Precision clock signals, usable as a base frequency source either directly, or converted (e.g., divided down) to some multiple of a base frequency source, can be generated from various circuits and configurations. One precision clock signal example is an atomic clock, so named as its signal is produced in response to the natural and quantum response of atoms or molecules, to an excitation source. In one approach, such atoms are in the form of alkali metals stored in a chamber, where the excitation source can be one or more lasers directed to the cell and the response of the chamber atoms is detected by measuring the amount of laser energy (photons) that passes through the chamber as the laser frequency sweeps across a range. In another approach, such molecules are in the form of dipolar gases also stored in a chamber, where the excitation source is an electromagnetic wave propagating through the chamber and the response of the chamber atoms is detected by measuring the amount of electromagnetic energy that passes through the chamber as the energy source sweeps across a range.

Further to the above, an example of a millimeter wave atomic clock is described in U.S. Pat. No. 9,529,334 (“the '334 Patent”), issued Dec. 27, 2016, hereby incorporated fully herein by reference, and which is co-assigned to the same assignee as the present application. The '334 Patent illustrates, among various other things, an atomic clock apparatus including a sealed cavity storing a dipolar gas, with an electromagnetic entrance into which an electromagnetic wave (or field) enters near a first end of the cavity and an electromagnetic exit from which an electromagnetic wave exits near a second end of the cavity. The electromagnetic wave that so exits is measured to determine an amount of absorption by (or transmission through) the dipolar gas, with the measure indicative of the quantum response of the gas as a function of the wave frequency. The '334 Patent also discusses a selection of pressure for the cavity-sealed dipolar gas, noting that pressure reduction below a desired pressure would reduce the magnitude of the peak response transition, thereby degrading the ability to detect and track the quantum response of the dipolar gas.

SUMMARY

In a clock apparatus, a signal waveguide includes: a gas cell having a sealed interior; and a dipolar gas inside the sealed interior. A first apparatus is configured to provide a first electromagnetic wave through the sealed interior along a first direction. A second apparatus is configured to provide a second electromagnetic wave through the sealed interior along a second direction, in which the second direction is opposite the first direction. Also, the clock apparatus includes receiving apparatus coupled to the signal waveguide and configured to detect an amount of energy in the second electromagnetic wave passing through the dipolar gas.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a schematic diagram of an example embodiment clock system.

FIG. 2 illustrates a method of operation of the system of FIG. 1 .

FIG. 3 illustrates a plot of the RX energy absorption signal in response to the energies E₁ and E₂ from the pump and probe of the system in FIG. 1 .

FIG. 4 again illustrates a schematic diagram of the FIG. 1 system with additional detail to a first example embodiment configuration for the bidirectional coupler.

FIG. 5 illustrates a schematic diagram of an alternative example embodiment clock system with pump and probe signals at respective longitudinal ends of the cell cavity.

FIG. 6 illustrates a schematic diagram of an alternative example embodiment clock system with a reflector at an opposing end of the cell cavity relative to the pump signal entrance to the cavity.

FIG. 7 illustrates a schematic diagram of an alternative example embodiment clock system with both the pump signal and receive signal passages departing away from the longitudinal axis of the cell cavity.

FIG. 8 illustrates a schematic and perspective diagram of an example embodiment configuration for a monolithically integrated bidirectional coupler and cavity.

FIG. 9 illustrates a schematic diagram of an alternative example embodiment with a circulating path and bidirectional travel of electromagnetic waves interrogating the dipolar gas.

FIG. 10 illustrates a schematic diagram of an alternative example embodiment with a circulating path and unidirectional travel of electromagnetic waves interrogating the dipolar gas.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

This description relates to precision frequency clock signals generated from molecular rotational quantum response in a cell, and more particularly to a system incorporating wave interrogation of the cell.

FIG. 1 illustrates a schematic diagram of an example embodiment clock system 10 ₁. Clock system 10 ₁ includes a gas cell 12, a bidirectional coupler 14, and a transceiver 16. Transceiver 16 provides a stable reference clock signal REFCLK in response to bidirectional electromagnetic interrogation of a dipolar gas in cell 12. Dipolar gas is preferred, because its electrical dipolar nature provides a detectable response to an interrogating electromagnetic wave, as described below.

Cell 12 is preferably formed in connection with an integrated circuit wafer, which can include multiple layers affixed relative to a semiconductor substrate (see, e.g., the incorporated by reference U.S. Pat. No. 9,529,334). In the illustration of FIG. 1 , and in various other drawings herein, the shape depicted of cell 12 depicts a generally top-down view, such as a planar cross-sectional view parallel to the plane generally defined by the substrate in which the gas storage cavity of cell 12 is formed. Generally, cell 12 includes a sealed enclosure having an interior in which a gas is stored. More specifically, cell 12 stores a dipolar gas, such as water vapor (H₂O), CH₃CN, HC₃N, OCS, HCN, NH₃, and isotopes of these gases, or any other dipolar molecular gas, inside an enclosed cavity of the cell, the cavity being sealed by nature of shapes, layering, and the like relative to the semiconductor substrate and layers that combine to enclose the dipolar gas at a relatively low (e.g., 0.1 mbar) pressure. For reasons described below, however, the enclosed pressure can be other than the example provided, as an example embodiment affords additional beneficial results that are independent of, or minimally affected by, the sealed pressure of the dipolar gas. Cell 12 also preferably includes, or is lined along most of its interior surfaces with, a material to facilitate the interior as a signal waveguide, where such material may be, for example, a conductor or a dielectric. Also, for reasons described hereinbelow, preferably cell 12 includes a majority longitudinal length having a linear axis 12 _(AX) and along which electromagnetic waves may travel, where the cross-sectional shape of cell 12 perpendicular to axis 12 _(AX) may be square, rectangular, trapezoidal, or still other shapes. The dimensions of cell 12 may vary, so for example it may be 30 to 150 mm long, 30 to 50 mm wide, and 0.5 millimeter tall, where selecting these or comparable sizes should preferably match properties for efficient wave propagation in view of the desired wave's frequency. Moreover, while the longitudinal shape is linear in FIG. 1 (and other drawings herein), it also may bend or turn so as to form, for example, a meandering path. In various embodiments, cell 12 includes an additional cavity portion that departs away from the linear portion of axis 12 _(AX), where in FIG. 1 , this non-coaxial or non-co-linear departure is shown generally at 12 _(DP).

Bidirectional coupler 14 provides structure, described below, for propagating electromagnetic waves in both directions along axis 12 _(AX) of cell 12. Accordingly, in the example of FIG. 1 , coupler 14 is connected to a probe antenna ANT_(TXPROBE) and to a pump antenna ANT_(TXPUMP). Probe antenna ANT_(TXPROBE) is positioned proximate a first passage 12 _(P1) of cell 12, so that electromagnetic energy from coupler 14 may be communicated to probe antenna ANT_(TXPROBE) and then into first passage 12 _(P1) as an entrance into cell 12 and thereby to pass in general in a first direction D₁ shown by a dashed arrow in FIG. 1 . In the context of first passage 12 _(P1), the term passage indicates a signal communications pathway for passage of the electromagnetic signal, but not an open aperture to ambient per se that otherwise could cause the sealed dipolar gas in cell 12 to escape; accordingly, such a pathway may be formed in various ways, such as by a glass layer as the upper surface of the sealed enclosure of the cell and providing an opening in the metal surround that is otherwise formed within the cell—in this manner, an electromagnetic signal may pass through the opening and glass into the interior of the cell, thereby reaching the dipolar gas sealed therein. Pump antenna ANT_(TXPUMP) is positioned proximate a second passage 12 _(P2) of cell 12, so that electromagnetic energy from coupler 14 may be communicated to pump antenna ANT_(TXPUMP) and then into second passage 12 _(P2) as an entrance into cell 12 and thereby to pass in general in a second direction D₂, also shown by a dashed arrow in FIG. 1 . Accordingly, for a majority 12 _(M) of the length along axis 12 _(AX), the signals communicated by coupler 14 provide bidirectional interrogation of the dipolar gas in cell 12.

Transceiver 16 is both for transmitting (TX) and receiving (RX) signals. Transceiver 16 includes four example blocks 18, 20, 22, and 24 for accomplishing the transceiver and signal responsiveness described herein. Accordingly, a signal generator 18 is connected, and is modulated by a modulator 20, to provide a base frequency controlled TX signal that, as described below, is swept across a particular frequency range from below to past the intrinsic quantum rotational state transition frequency for the dipolar gas in cell 12 (e.g., 183.31 GHz for water). Modulator 20 modulates the frequency of the interrogation signal provided by the signal generator 18. The modulation frequency ranges, for example, between 10 to 50 KHz. After the signal passes through the gas cell, it is received by a lock in amplifier 22, via an input 16 _(IN) coupled to receive the RX signal from a receive antenna ANT_(RX). Particularly, antenna ANT_(RX) is positioned proximate a third passage 12 _(P3) of cell 12, so that electromagnetic energy from along axis 12 _(AX) may be communicated from passage 12 _(P3), as an exit, to receive antenna ANT_(RX) and then to transceiver 16 and, more particularly, to lock in amplifier 22. Generally, lock in amplifier 22 uses the signal from the modulator 20 to measure the RX signal at the same modulation frequency provided by modulator 20. In this way, lock in amplifier 22 is able to reject noise outside the modulation frequency and thereby reduce the noise from the system.

The TX signal may be a sinusoid, although other periodic oscillating signals also may be used, so long as such signal includes a Fourier component in the frequency of interest. The TX signal is connected, via an output 16 _(OUT), to bidirectional coupler 14. Under feedback control, signal generator 18 also provides the ultimately-refined reference clock REFCLK. The RX signal represents an amount of the originally transmitted signal TX that passes through cell 12 and contains the information of the absorption of the dipolar gas at the quantum rotations transition frequency. In response, lock in amplifier 22 provides a signal that is the first derivative of the signal as it is swept in frequency. Consequently, at the frequency corresponding to the quantum rotational molecular transition, the first derivative is zero, and the error signal ERR is zero. At frequencies different from the quantum rotational transition, the signal ERR is not zero and provides a correction to the loop filter 24, allowing it to “lock” the clock to the quantum transition frequency. This apparatus also filters out noise as detected by reference to the modulation frequency provided by modulator 20. In one example, lock in amplifier 22 provides the error signal ERR as an in-phase output, and the error signal ERR is used as an input by a loop filter 24 (or controller circuit) for providing a control output signal CO to signal generator 18. As further described below, such feedback selectively adjusts the TX output signal frequency, following an initial sweep, to ultimately maintain this frequency at a peak absorption frequency of the dipolar molecular gas inside the sealed interior of cell 12, with that maintained frequency providing a stable output reference clock REFCLK. In some examples, the RF power of the TX and RX loop is controlled so as to avoid or mitigate stark shift effects (frequency shifts in response to quantum transition produced by the presence of an electric field).

The overall operation of system 10 ₁ is described in connection with the flow chart method 30 of FIG. 2 . Method 30 is shown as a sequential flow process for sake of discussion, while in general the steps provide a feedback control and, accordingly, each step may actually occur in a time overlapping one or more of the other steps. In a step 32, transceiver 16 sweeps the modulated base frequency TX signal, so the base frequency is swept across an initial frequency range FR that includes the intrinsic quantum rotational state transition frequency for the dipolar gas in cell 12. Thus, in the example where the dipolar gas is water, the range will include the intrinsic quantum rotational state transition frequency of 183.31 GHz for water, and could include, for example, a sweep from 183.28 GHz to 183.34 GHz. Thus, the TX signal delivers an energy E to bidirectional coupler 14, sweeping across this frequency range, so that the same frequency is simultaneously applied by both antennas ANT_(TXPUMP) and ANT_(TXPROBE), so as to achieve the bidirectional propagation along directions D₁ and D₂ introduced above. Also, while the TX signal represents a certain amount of energy E, preferably coupler 14 couples a first amount E₁ of that energy to antenna ANT_(TXPROBE) and a second amount E₂ of that energy (i.e., subject to possible signal loss TX−E₁=E₂) to antenna ANT_(TXPUMP). Preferably E₂>E₁, where for example E₂ may be 90% of TX, leaving 10% of TX as E₁.

In step 34, transceiver 16 converges to, or locks in at, a Doppler free frequency f_(T) at which peak absorption of the electromagnetic wave occurs in the dipolar gas sealed in cell 12, in response to the sweeping frequency from step 32 and the corresponding detected response. Particularly, steps 32 and 34 may essentially occur simultaneously, as during step 34, receive antenna ANT_(RX) couples the RX signal, which occurs from the TX signal of step 32, to lock in amplifier 22. Lock in amplifier 22 also receives the modulation frequency from modulator 20, so that according to lock-in methodology, noise may be reduced from the received signal so as to detect the received energy corresponding to the base frequency TX signal that is input to cell 12 from signal generator 18. Further, lock in amplifier 22 (or associated circuitry) evaluates a derivative of the RX signal as the step 32 sweep occurs. Accordingly, as the RX signal is changing (in response to a quantum response in cell 12), the derivative is non-zero, whereas as the RX signal reaches a peak (maximum or minimum) the derivative approaches or is zero. This derivative determination provides an error signal ERR, connected as an output to loop filter 24, and as further explained below the error ERR signal is expected to reach zero at three different TX base frequencies.

In step 36, loop filter 24 provides a control signal CO to signal generator 18, so as to refine control of signal generator 18 to make adjustments in the frequency of TX to restrain or refine that frequency in a feedback look controlled manner to thereafter maintain the base frequency of TX at the center frequency among the three different TX base frequencies for which the error signal ERR is zero. This center frequency represents the frequency f_(T) at which peak absorption occurs of the electromagnetic wave occurs in the cell dipolar gas. In this regard, loop filter 24 is preferably a proportional integral derivative (PID) circuit, with an output that sums values, multiplied times respective controlled parameters, corresponding to the three factors (i.e., proportional, integral, derivative) that give the PID circuit its name. Accordingly, the output of loop filter 24 facilitates a clock signal with good stability and reduces or eliminates the possibility of the signal generator creating a signal that oscillates around the around desired frequency. Accordingly, at this point, the TX signal should maintain a base frequency at or near the intrinsic transitional quantum frequency of the dipolar gas, and that same base frequency is output as the reference clock signal REFCLK, as may be used by other circuitry requiring a frequency-precise clock signal. Indeed, method 30 may be regarded as an ongoing loop running at selected (or all) times that the clock is operational and endeavoring to lock the clock at most or all instants where, once locked after an initial scan of steps 32 and 34, the loop continues to perform across a second frequency range that is smaller in bandwidth than the above-described step 32 initial frequency range FR, where the second frequency range is expected to still include the center frequency representing frequency f_(T). Accordingly, the step 32 sweep and step 34 response detection can essentially repeat in step 36, but using a narrower bandwidth for more efficient refinement or maintenance of the base frequency at the peak absorption frequency f_(T), as further described hereinbelow.

Given the preceding, system 10 ₁ facilitates electromagnetic interrogation of the dipolar gas within cell 12, by transmitting TX at varying (e.g., sweeping) frequencies within a defined band around a suspected quantum absorption frequency at which the transmission efficiency of cell 12 is minimal (absorption is maximal), and when the system detects a null or minima in transmission energy (or maximum in absorption), the TX output signal frequency is regulated to operate at the frequency so detected, thereby in response to the natural quantum behavior of the dipole. As a result, REFCLK, like that quantum behavior, is generally stable with respect to time (does not degrade or drift over time) and is largely independent of temperature and a number of other variables.

The Allan deviation (which is the square root of the Allan variance) is a measure of frequency stability of clock signals (e.g., in clocks, oscillators, amplifiers), and in effect is a measure of frequency distribution over a number of samples—so if the Allan deviation measure is lower, then the variance of distribution is lower, and the performance of the clock signal is better. Further, the Allan deviation is inversely proportional to both the quality factor (Q) and signal-to-noise ratio (SNR) of the frequency response curve (such as in transceiver 16), as it processes the received RX signal response to detect an absorption peak frequency. Thus, by increasing one or both of the Q and SNR of the system, the Allan deviation measure is improved. One approach can achieve certain improvement in the Allan deviation by reducing pressure within the cell, which reduces the width of the transition caused by pressure broadening phenomena, as such an approach will improve Q only down to a certain pressure. But for pressures below a certain value (e.g., 0.1 mbar), the width cannot be reduced further because of Doppler broadening, which is independent of pressure and mostly dependent on the temperature of the gas. However, pressure reduction reduces the number of molecules available for interrogation, thereby reducing the amplitude of the quantum transition signal. Accordingly, an optimum pressure can be found (for water this pressure is approximately 0.1 mbar) where the SNR can be maximized by having the minimum transition width possible and the maximum amplitude possible.

As described above, Doppler broadening is an effect caused by the distribution of velocities of atoms/molecules, especially in response to higher temperatures. Particularly, for atoms having velocities in a same direction as the direction of propagation of the electromagnetic wave, the Doppler effect will cause the transition of the dipolar molecules from the lower energy vibrational state to the higher energy vibrational state to occur when the frequency of the electromagnetic signal is lower than the frequency that corresponds to the energy difference of the two vibrational states (E=h f) (e.g., 183.31 GHz for water). Conversely, for atoms having velocities in an opposing direction as the unidirectional signal, the Doppler effect will cause the rotational transition of those atoms to occur at an excitation frequency that is higher than the intrinsic quantum rotational state transition frequency for the dipole. Thus, the result of Doppler spreading is a wider spectral line when interrogating these atoms/molecules, which accordingly provides less accuracy in identifying a particular frequency of quantum transition.

The contrast of example embodiment benefits, particularly in connection with the description above and the example embodiment implementation of bidirectional signal paths along majority 12 _(M) of cell 12, are further shown by the plot of FIG. 3 . Specifically, FIG. 3 illustrates a plot of the RX energy absorption by the gas in cell 12, in response to the energies E₁ and E₂ from the pump and probe TX signals, respectively, and as a function of frequency. Both the probe and pump are at the same frequency, and that frequency is swept across a range that includes the intrinsic quantum rotational state transition frequency f_(T) for the dipole (e.g., 183.31 GHz for water). Generally, therefore, the sweeping of frequency may be low to high (or high to low), producing the response shape depicted in FIG. 3 . While FIG. 3 plots absorption, transmission energy is provided in the signal TX and detected in the signal RX, so a plot, normalized to a value of one, is essentially one minus the signal plot of FIG. 3 . In any event, as the swept frequency approaches the intrinsic quantum rotational state transition frequency, the absorption of energy by the dipolar gas increases as shown (or the amount of energy transmitted through the cell decreases), and as detected in the RX signal, creates an absorption spectra that is flatter away from that intrinsic frequency and that ascends from both directions as the frequency sweep nears the dipolar gas intrinsic frequency. Additionally, as the intrinsic frequency is approached, a first peak PK₁ occurs which is shown as a maximum in terms of energy absorption and at a frequency below the Doppler free frequency f_(T), and similarly above f_(T) a second peak PK₂ occurs. As further described below, however, example embodiments are able to detect an additional peak as the Doppler free frequency f_(T), between peaks PK₁ and PK₂.

Further regarding the FIG. 3 response, an example embodiment provides one of the bidirectional TX signals at a higher energy than the other, where for sake of convention in other technologies the higher-energized signal is termed the pump. As a result, it is anticipated in connection with some example embodiments that most of the atoms interrogated by the higher-energized pump signal, at the appropriate quantum frequency, will be excited to an energy level higher than a lower energy (e.g., ground) state, while other of the atoms will remain at the lower energy state. Thus in response to the probe signal, the number of molecules that are in the ground state is significantly reduced because most of them have been excited to the excited state by the pump signal causing a decrease in the absorption profile. Also, however, the bidirectional or counter-propagating nature of the probe and pump signals also reduces or eliminates the Doppler effect. Particularly, atoms at zero velocity experience do not have the Doppler effect, and are accordingly affected by the frequency aspect of both of the counter-propagating waves, where again the pump beam has depopulated a portion of the ground state to the higher energy state. Accordingly, less of the ground state atoms remain at frequency f_(T), so fewer atoms remain to absorb the probe energy and a corresponding drop in absorption, where such lack of absorption of that probe energy is shown in the resultant RX plot of FIG. 3 , which includes a dip DP centered around at the intrinsic frequency f_(T), the dip arising from the fewer low-energy atoms to absorb the probe signal. Thus, the example embodiment provides so-called Doppler-free spectroscopy, in that Doppler broadening is no longer an issue under this approach and the benefit in some embodiments may be independent of the gas pressure in cell 12. The frequency width Δf_(DP), between peaks PK₁ and PK₂, DP is considerably less than the frequency width Δf_(O) of the outer Gaussian ascending portions of the plot; thus, the Q relative to the frequency width Δf_(DP) is considerably better than the Q relative to the frequency width Δf_(O) of the outer ascending portions. Accordingly, the improved Q of the Doppler free architecture improves the Allan deviation of system 10 (and the other comparable systems described in this document).

FIG. 4 again illustrates a schematic diagram of system 10 ₁, with additional detail provided for one example embodiment configuration for bidirectional coupler 14. While FIG. 4 illustrates blocks in certain aspects, the top-down spatial relationship may be illustrative of an example embodiment implementation in general in that cell 12, coupler 14, and transceiver 16 may be positioned relative to one another, or at least proximate one another, in connection with a semiconductor substrate and/or wafer. For example, cell 12 may be formed as part of layering affixed to, or part of, the semiconductor substrate, with an upper layer thereof having passages (not shown, but see FIG. 1 , passages 12 _(P1), 12 _(P1), and 12 _(P3)) being penetrable by electromagnetic waves, such as by way of a glass layer having a conductive layer adjacent thereto and with apertures, corresponding to the passages, formed in the conductive layer. Further, coupler 14 is then formed proximate (e.g., within 5 millimeters) cell 12, being located as close as possible to reduce losses of the signal traveling from the directional coupler and cell 12. Coupler 14 may be formed by members (e.g., conductors, described below) applied (e.g., surface plated) to an upper surface of the above-described glass layer that encloses the dipole-retaining sealed cavity of cell 12. Alternatively and as shown in FIG. 8 , coupler 14 may be coplanar with cell 12 or monolithically integrated into the same cavity that forms cell 12. Lastly, transceiver 16 can be formed as a separate integrated circuit, which is then conductively and mechanically affixed nearby coupler 14 and cell 12; indeed, while not shown, transceiver 16 may be spatially affixed above either or both of cell 12 and coupler 14, via wire bonding, flip chip, or other packaging techniques.

Referring in more detail to coupler 14 of FIG. 4 , in an example embodiment, illustrated in FIG. 4 , coupler 14 includes two conductors 14 ₁ and 14 ₂, which preferably have like dimensions and represent mirror-image symmetric structures about an imaginary linear axis 14 _(AX), but the two are otherwise physically isolated from one another. For example, each of conductors 14 ₁ and 14 ₂ may be formed by fabrication techniques, which for example may include processes for patterning and affixing metallic surfaces atop a layer. For example, the layer may be glass, with a common ground metallization below the entirety of coupler 14. Further, such formation facilitates fabrication and signal coupling between the conductors. Particularly, the full 100% energy of the TX signal from transceiver is preferably connected to a first end 14 _(2E1) of conductor 14 ₂, while a second end 14 _(2E2) of conductor 14 ₂ is connected to the pump antenna ANT_(TXPUMP). Meanwhile, a low voltage signal, such as ground, is connected to a first end 14 _(1E1) of conductor 14 ₁, while a second end 14 _(1E2) of conductor 14 ₂ is connected to the probe antenna ANT_(TXPROBE) In this configuration, a portion of the TX signal energy is coupled, for example capacitively, inductively, or through other manner, from conductor 14 ₂ to conductor 14 ₁, where preferably those conductors are dimensioned, positioned, and otherwise coupled so that approximately 90% of the energy of the TX signal remains in conductor 14 ₂, while 10% of the energy of the TX signal is coupled to conductor 14 ₂. Thus, the pump antenna ANT_(TXPUMP) provides an energy E₂ of 90% of the TX signal in a first direction through cell 12, while the probe antenna ANT_(TXPROBE) provides an energy E1 of 10% of the TX signal in a second direction, opposite the first, through cell 12. Lastly, in connection with the construction of coupler 14, preferably the linear distances (along which the pump and probe signals are to propagate) are all preferably integer multiples of ½ of the wavelength of the RF signal to be propagated through cell 12. For example, FIG. 4 illustrates dimensions DM₁ and DM₂, as linear structural paths for wave propagation, that is, each linear path is a segment of the total propagation path, where the segment is linear for the respective path. Such dimensions are likewise preferable for other like linear paths in coupler 14, namely, dimensioned in accordance with this stated proportionality relative to the RF signal wavelength.

FIG. 5 illustrates a schematic diagram of an alternative example embodiment clock system 10 ₂. Also, transceiver 16 is shown in a simplified view. Where system 10 ₂ differs from system 10 ₁ is the positioning of certain antennas relative to the second and third passages 12 _(P2) and 12 _(P3) of cell 12. Particularly, in system 10 ₂, while the probe antenna ANT_(TXPROBE) remains proximate first passage 12 _(P1), the other two antennas are switched in location, that is, the RX antenna ANT_(RX) is proximate second passage 12 _(P2) and the pump antenna ANT_(TXPUMP) is proximate third passage 12 _(P3). In this manner, the bidirectional or counter-propagating signals will pass along the entirety 12 _(E) of axis 12 _(AX), as opposed to only a majority portion 12 _(M) thereof as was the case for system 10 ₁. However, for system 10 ₂, the receive antenna passage (12 _(P2)) is no longer co-linear with axis 12 _(AX), but instead the signal is received and communicated to transceiver 16 from the non-axial departure 12 _(DP) portion of cell 12.

FIG. 6 illustrates a schematic diagram of an alternative example embodiment clock system 10 ₃, which again shares various attributes with embodiments described above. Where system 10 ₃ differs from system 10 ₂, however, is the elimination of an external probe transmit antenna (see, e.g., ANT_(TXPROBE) in systems 10 ₁ and 10 ₂) and of its respective passage 12 _(P1) (see, FIGS. 1 and 5 ), so electromagnetic waves are communicated into cell 12 by only a single transmit antenna ANT_(TX), so system 10 ₂ does not include two separate, albeit different energy level, transmitters and corresponding transmission passages into the cell. Instead, transceiver 16 directly couples a TX signal, without an intermediate coupler (see, e.g., coupler 14 of FIG. 1 ), to a transmit antenna ANT_(TX). Further, the single transmit antenna ANT_(TX) is proximate a passage 12 _(P3) of cell 12. Further, while cell 12 still includes a passage 12 _(P3) at a first longitudinal end of the linear pathway in the cell, at an opposing second longitudinal end is located an electromagnetic wave reflector 12 _(EWR). Given this difference and the description above, when the pump antenna ANT_(TXPUMP) transmits energy into passageway 12 _(P3) as an entrance into cell 12, that energy proceeds in direction D₁ from the first longitudinal end of the linear pathway toward the second longitudinal end of the linear pathway, where a portion of that energy is reflected toward the first longitudinal end of the linear pathway, that is, back along direction D₂. Moreover, in this example embodiment, reflector 12 _(EWR) is structured (e.g., by material, shape, dimension and the like) so as to reflect a considerably reduced energy E₁ of energy, as compared to the level of energy E₂ received from pump antenna ANT_(TXPUMP). Accordingly, and consistent with example embodiments described above, such reflection may be that energy E₁ provides approximately 10% of the total energy received by cell 12 from the TX signal. The remaining structure and operation of cell 10 ₃, however, is readily comparable to other aspects already described.

FIG. 7 illustrates a schematic diagram of an alternative example embodiment clock system 10 ₄, which has various points in common with other example embodiments herein. Where system 10 ₄ differs is that cell 12 is symmetric about its axis 12 _(AX), in that it includes a longitudinal cavity across a majority 12 _(M) of its overall length, but it has equally shaped and sized departure cavity portions 12 _(DP1) and 12 _(DP2), each with a respective passage 12 _(P3) and 12 _(P2), for communicating respective electromagnetic signals between cell 12 and the pump antenna ANT_(TXPUMP) and RX antenna ANT_(RX), respectively. The majority length longitudinal cavity supports an area where the pump and probe signal coexist and where the zero velocity molecules are detected and contribute to the strength of the signal. Accordingly, if this section is longer, then the signal is larger, thereby contributing to a better SNR.

FIG. 8 illustrates an electrical block and perspective diagram of an alternative example embodiment clock system 10 ₅, in which a channel 800 is formed as a recessed path in a substrate 802, whereby channel 800 includes portions that are comparable in certain respects to cell 12 and coupler 14 of embodiments described above. Accordingly, cell 12 and coupler 14 are monolithically integrated into a same layer in substrate 802 (e.g., co-planar), as now described. Particularly, channel 800 includes various portions, which are generally indicated with brackets so as to illustrate functionality, but in the illustrated example the entire channel 800 functions as a gas cell, that is, a sealed enclosure for storing atoms to be interrogated by an electromagnetic wave. In this regard, while not shown, an additional layer (e.g., glass) is disposed atop an upper surface of substrate 802, thereby enclosing the sealed gas while also allowing receipt of a TX signal from transceiver 16 and providing a path for wave propagation after which the signal provides an RX signal back to transceiver 16. In one portion of channel 800 shown generally by the bracket and coupler reference of 14, there are two proximate wave paths 14 _(P1) and 14 _(P2) that are in fluid communication with one another, with a sidewall aperture coupler 14 _(C) portion in which a number of apertures are formed between the two paths; in this manner, as TX energy enters channel 800, a first portion (e.g., pump at 90%) of that energy passes through path 14 _(P1) and the remaining portion (e.g., probe at 10%) of that energy passes through the apertures in sidewall aperture coupler 14 _(C) and then through path 14 _(P2). Paths 14 _(P1) and 14 _(P2) continue to, and are also in fluid communication with, opposing ends of a meandering cell portion 12 _(P). Accordingly, in cell portion 12 _(P), as in embodiments described above, bidirectional interrogation occurs as the pump wave passes in a first direction through portion 12 _(P), while the probe wave passes in a second direction, opposite the first direction, also through portion 12 _(P), thereby bidirectionally interrogating dipolar gas in portion 12 _(P). Finally, some of the energy of the propagating wave is able to pass from portion 12 _(P), back to transceiver 16, in the form of the RX signal from an end 800 _(E) of channel 800.

FIG. 9 illustrates a schematic diagram of an alternative example embodiment clock system 10 ₆. Again, transceiver 16 is shown in a simplified view. Also generally, system 10 ₆ operates according to method 30 shown in FIG. 3 . Where system 10 ₆ differs from example embodiments described above, however, is that cell 12 includes a continuous chamber portion 12 _(CCP), in which electromagnetic waves may enter cell 12 and continue to circulate to return toward, and then again pass beyond, a point at which they entered the chamber, as is now further described. First, as with system 10 ₁, system 10 ₆ again includes a probe antenna ANT_(TXPROBE) proximate a first passage 12 _(P1), a pump antenna ANT_(TXPUMP) proximate a second passage 12 _(P2), and an RX antenna ANT_(RX) proximate a third passage 12 _(P3). However, each of those passages is in a respective extension portion of cell 12, shown as portions 12 _(EP1), 12 _(EP2), and 12 _(EP3). In an embodiment, each of extension portions 12 _(EP1), 12 _(EP2), and 12 _(EP3) is in fluid communication with continuous chamber portion 12 _(CCP). An alternative embodiment may maintain the gas solely (or predominantly) in the continuous chamber portion 12 _(CCP), but this will require some type of hermetic window between the extension portions and the circular portion. Such a window would introduce losses in the signal path and potential undesirable reflections, degrading device performance.

In system 10 ₆, an electromagnetic signal is transmitted from ANT_(TXPROBE), via first passage 12 _(P1) into cell 12, that signal propagates as a wave along the interior of extension portion 12 _(EP1) in a direction D₁, and it continues into continuous chamber portion 12 _(CCP) so that direction D₁ thereby can be characterized as counterclockwise in FIG. 9 . Due to the continuous nature of portion 12 _(CCP), however, which in the illustrated example is by way of a circular cross-section when sectioned across a plane along the direction of the circulation around the entire structure, then as the wave passes 360 degrees it will reach the point at which it entered into the circular region, that is, where extension portion 12 _(EP1) communicates with the circular portion of cell 12, and then continue onward to again circulate in the counterclockwise direction D₁. Similarly, but in an opposite direction, as an electromagnetic signal is transmitted from ANT_(TXPUMP), via second passage 12 _(P2), into cell 12, that signal also propagates as a wave along extension portion 12 _(EP2), but in a direction D₂, opposite that of D₁, and thus in chamber continuous portion 12 _(CCP) at which point the direction D₂ is clockwise in FIG. 9 . Further, again the continuous nature of portion 12 _(CCP) facilitates an ongoing circulation of the wave, so that as it passes 360 degrees through cell 12 it will reach the point at which it entered into the circular region, that is, where extension portion 12 _(EP2) communicates with the circular portion of cell 12, and then continue onward to again circulate in the clockwise direction D₂.

The number of wave circulations facilitated in an example embodiment, may repeat a number of times, effectively providing a wave interrogation of the dipolar gas molecules along an effective length far in excess of a single path interrogation along the circumference of portion 12CCP.

The number of circulations will be a function primarily of the quality factor of the cavity (not to be confused with the quality factor of the quantum absorption). The quality factor of an electromagnetic cavity is defined by the ratio of energy stored in the resonator to the energy supplied to it. Accordingly, the more efficient (better performing) the walls of the cavity in communicating the wave through the cavity, the better will be the confinement and the better will be the quality factor of the cavity and the larger will be the number of circulations. The circulation number could be even in excess of 100 circulations under resonance conditions, as can be confirmed, for example, by evaluating strength of a given energy signal in the dipolar gas. Also recognized, however, is that a detrimental effect may occur if the cavity quality factor is above a particular threshold. In example embodiment methodology, therefore, a cavity may be implemented and tested for a power broadening effect, as may be detected, for example, from an increase in the width of the quantum transition, reducing the transition quality factor. Such an effect may occur when power applied by the transmitter is increased, or the intensity of the electric field in the cavity reaches high values due to high quality factor of the cavity. Increasing power in this way could be considered an effective way to improve device performance so as to increase SNR, but such power may concurrently diminish the Q of the response curve. And because Allan deviation is inversely proportional to both SNR and Q of the frequency response curve, a point of diminishing return is reached if SNR increases by a percentage that exceeds a comparable percentage decrease in Q that was caused by the SNR increase—so optimum performance is achieved in the example embodiments by maximizing the product of SNR and Q. Accordingly, in an example embodiment, a cell design may be created and tested at increasing levels of TX energy, and if it is found that an increased signal energy is causing too much power broadening so as to undesirably reduce Q beyond an acceptable level, then that effect may be reduced by diminishing the quality factor of the cell design. Example embodiments to accomplish such quality factor reduction may be achieved by making the walls of the cavity less efficient, for example by making adding roughness to the walls or using higher resistivity metals (e.g., switching from gold to aluminum). Example embodiments include a roughness of 500 Angstroms, but alternatives are contemplated with a roughness greater than 500 Angstroms, and up to 2 micrometers.

Given the structure of system 10 ₆, as waves circulate as described above, a portion of the energy will exit the circular cross-sectioned portion of cell 12, via extension portion 12 _(EP3), to third passage 12 _(P3), and a portion of that energy is thereby communicated to antenna ANT_(RX) and then be received by transceiver 16, consistent with above-described embodiments. However, the nature of a continuous passage causes the remaining energy of the wave to continue to circulate multiple times through the passage, thereby providing additional energy opportunities to interrogate the dipolar gas cells within cell 12. As a result, the number of molecules interrogated is increased, thereby improving the SNR performance as compared to a single-pass interrogation system, and advancing toward near saturation operation. Moreover, by using a pump and probe architecture, the system provides a Doppler free transition.

In another aspect of system 10 ₆, in an example embodiment, the shape and dimensions of cell 12, and particularly its chamber continuous portion 12 _(CCP), are preferably selected to facilitate resonance of the wave passing therethrough and to circulate a number of times. For example, FIG. 9 illustrates the circular portion outer diameter 12 _(OD) and inner diameter 12 _(ID). These two dimensions are preferably selected to achieve a waveguide suitable for the band of interest (e.g., the WR-5 band of 140-220 GHz). Further, for the specific operating frequency, a propagating wave will exhibit a specific guided wavelength, λ_(g), inside the waveguide and that can be different from unguided waves, and λ_(g) can be determined experimentally or through computer simulations. Given these parameters, and in order to provide beneficial energy for interrogating the dipolar gas, in an example embodiment the diameter of chamber continuous portion 12 _(CCP) is dimensioned according to the following Equation 1:

$\begin{matrix} {D_{m} = \frac{N\lambda_{g}}{\pi}} & {{Equation}1} \end{matrix}$

where,

-   -   D_(m) is the middle diameter of portion 12 _(CCP), that is, the         distance halfway between outer diameter 12 _(OD) and inner         diameter 12 _(ID) (i.e., D_(m)=(12 _(OD)+12 _(ID))/2);     -   N is an integer of 1 or greater; and     -   λ_(g) is the above-introduced guided wavelength of the wave         through chamber continuous portion 12 _(CCP).         Thus, with Equation 1 providing for a middle diameter D_(m) of         cell 12, it is anticipated that as the wave circulates         repeatedly an integer number of times around chamber continuous         portion 12 _(CCP) (passing a point from which it earlier entered         portion 12 _(CCP) started or previously passed), the wave energy         will be constructive in phase, so as to provide beneficial         signal performance.

Further in connection with FIG. 9 , the circular nature (when considered in the plane of the FIG. 9 ) of cell 12 is an example, and other continuous paths that permit a wave to circulate as described also are contemplated. For example, the continuous path may lie along an oval or a generic polygon. Also in this regard, Equation 1 defines a diameter D_(m) as it relates to a circular perimeter for the continuous path, given that a diameter of a circle is its perimeter divided by pi. For the more general case of a continuous path having a perimeter P, Equation 1 may be rewritten as the following Equation 2:

P=Nλ _(g)  Equation 2

Accordingly, for example embodiments with a chamber continuous portion that is non-circular, Equation 2 sets forth a preferred perimeter for that portion. Lastly in connection with FIG. 9 , the cross-sectional shape of continuous path 12 _(CCP), taken perpendicular to the direction of wave propagation, also may be selected from various shapes. For example, the cross-sectional shape of cell 12 in FIG. 9 , perpendicular to direction D₁ (or D₂) may be square, rectangular, trapezoidal, or still other shapes.

FIG. 10 illustrates a schematic diagram of an alternative example embodiment clock system 10 ₇, which in various respects is comparable to system 10 ₆ of FIG. 9 . Also generally, system 10 ₇ operates according to method 30 shown in FIG. 3 . Where system 10 ₇ differs from example embodiments described above, however, is that electromagnetic waves are communicated into cell 12 by only a single transmit antenna ANT_(TX), so system 10 ₇ does not include two separate, albeit different energy level, transmitters and corresponding transmission passages into the cell. Instead, transceiver 16 directly couples a TX signal, without an intermediate coupler (see, e.g., coupler 14 of FIG. 1 ), to a transmit antenna ANT_(TX). Further, the single transmit antenna ANT_(TX) is proximate a passage 12 _(P1) that is located in an extension portion 12 _(EP1) of cell 12, where the extension portion, as was the case with system 10 ₆ of FIG. 9 , fluidly communicates with a continuous chamber portion 12 _(CCP). Portion 12 _(CCP) again is preferably circular in cross-section taken along a plane of wave travel and has a middle diameter D_(m), as may be established pursuant to the above-described Equation 1. As a result, an electromagnetic signal transmitted from antenna ANT_(TX), via passage 12 _(P1) into cell 12, propagates as a wave along the interior of extension portion 12 _(EP1) in a direction D₁, and it continues into continuous chamber portion 12 _(CCP) so that direction D₁ thereby can be characterized as clockwise in FIG. 10 . Moreover, because of the continuous nature of portion 12 _(CCP), and further contributed by the preferred dimension of its middle diameter, the wave will circulate in a constructive manner in cell 12, thereby interrogating an ample amount of dipolar gas in the process. And such a result is achieved even through the path of the electromagnetic wave is omnidirectional, as opposed to the bidirectional signal travel in various embodiments described above. Accordingly, the response of such interrogation will have an improved SNR as received by transceiver 16, via the exit extension portion 12 _(EP2), passage 12 _(P2), and receive antenna ANT_(RX).

As described above, various example embodiments provide a system generating frequency clock signals from atomic rotational quantum response in a cell using bidirectional wave interrogation of the cell. For example, Q factor of the system response is improved (increased), thereby correspondingly improving Allan deviation.

Also, as described above, various example embodiments provide a system generating frequency clock signals from atomic rotational quantum response in a cell using a continuous chamber providing a circulating interrogation of the cell. For example, SNR of the system response is improved. Moreover, the system may perform well independent of pressure of the (e.g., dipolar) gas stored in the cell.

Modifications are possible in the described embodiments, and other embodiments are possible, within the scope of the claims. 

What is claimed is:
 1. An apparatus comprising: a sealed container containing a dipolar gas; a first transmit antenna, a second transmit antenna, and a receive antenna each communicatively coupled to the sealed container; and a control circuit including a transceiver, the control circuit having a first transmit output, a second transmit output, and a receive input, the first transmit output coupled to the first transmit antenna, the second transmit output coupled to the second transmit antenna, and the receive input coupled to the receive antenna.
 2. The apparatus of claim 1, wherein the control circuit is configured to provide a first signal at the first transmit output, and provide a second signal at the second transmit output; and wherein the first transmit antenna is configured to transmit the first signal in the sealed container in a first direction, and the second transmit antenna is configured to transmit the second signal in the sealed container in a second direction opposite to the first direction.
 3. The apparatus of claim 1, wherein the control circuit includes a bi-directional coupler having a coupler input, a first coupler output, and a second coupler output, the first coupler output coupled to the first transmit output, and the second coupler output coupled to the second transmit output; and wherein the transceiver includes: a signal generator having a first output, a reference clock output, and a control input, the first output coupled to the coupler input; and a lock in amplifier having an amplifier input and an amplifier output, the amplifier input coupled to the receive input, and the amplifier output coupled to the control input.
 4. The apparatus of claim 3, wherein the control input is a first control input, the amplifier input is a first amplifier input, the signal generator has a second control input, the lock in amplifier has a second amplifier input, and the control circuit includes a modulator having a first modulator output coupled to the second control input and a second modulator output coupled to the second amplifier input.
 5. The apparatus of claim 4, further comprising an error processing circuit coupled between the amplifier output and the first control input.
 6. The apparatus of claim 5, wherein the error processing circuit includes at least one of: a filter, or a proportional integral derivative (PID) circuit.
 7. The apparatus of claim 3, wherein the bi-directional coupler includes a pair of coupled conductors.
 8. The apparatus of claim 3, wherein the bi-directional coupler includes a sidewall aperture coupler.
 9. The apparatus of claim 3, wherein the bi-directional coupler is configured to: receive a first signal at the coupler input; provide the first signal at the first coupler output; and provide a second signal as an attenuated version of the first signal at the second coupler output.
 10. The apparatus of claim 1, wherein the control circuit has a clock output.
 11. The apparatus of claim 1, wherein the control circuit is configured to: provide a first signal at the first transmit output; provide a second signal at the second transmit output; receive a third signal at the receive input; determine, based on the third signal, a first frequency of a first peak absorption of the first and second signals by the dipolar gas; determine, based on the third signal, a second frequency of a second peak absorption of the first and second signals by the dipolar gas; determine a third frequency based on the first and second frequencies; and provide a fourth signal having the third frequency at the clock output.
 12. The apparatus of claim 1, wherein the sealed container has a longitudinal portion and a branch portion.
 13. The apparatus of claim 12, wherein the first transmit antenna is communicatively coupled to the branch portion, and the second transmit antenna and the receive antenna are communicatively coupled to the longitudinal portion.
 14. The apparatus of claim 12, wherein the first and second transmit antennas are communicatively coupled to the longitudinal portion, and the receive antenna is communicatively coupled to the branch portion.
 15. The apparatus of claim 12, wherein the branch portion is a first branch portion, and the sealed container has a second branch portion, the first and second branch portions extending towards opposite sides of the longitudinal portion.
 16. The apparatus of claim 15, wherein the first transmit antenna is communicatively coupled to the longitudinal portion, the second transmit antenna is communicatively coupled to the first branch portion, and the receive antenna is communicatively coupled to the second branch portion.
 17. The apparatus of claim 1, wherein the sealed container has a circular portion, a first branch portion, a second branch portion, and a third branch portion; and wherein the first transmit antenna, the second transmit antenna, and the receive antenna are communicatively coupled to, respectively, the first branch portion, the second branch portion, and the third branch portion.
 18. The apparatus of claim 17, wherein the control circuit is configured to provide a first signal at the first transmit output, and provide a second signal at the second transmit output, the first and second signals having a particular wavelength when propagating in the dipolar gas; and wherein a diameter of the circular portion is based on the wavelength.
 19. An apparatus comprising: a sealed container containing a dipolar gas, the sealed container having a branch portion and a longitudinal portion; a transmit antenna communicatively coupled to a first end of the longitudinal portion; a receive antenna communicatively coupled to the branch portion; and an electromagnetic reflector at a second end of the longitudinal portion, the second end being opposite to the first end; and a control circuit including a transceiver, the control circuit having a transmit output and a receive input, the transmit output coupled to the transmit antenna, and the receive input coupled to the receive antenna.
 20. An apparatus comprising: a sealed container containing a dipolar gas, the sealed container having a circular portion, a first branch portion, and a second branch portion; a transmit antenna communicatively coupled to the first branch portion; a receive antenna communicatively coupled to the second branch portion; and a control circuit including a transceiver, the control circuit having a transmit output and a receive input, the transmit output coupled to the transmit antenna, and the receive input coupled to the receive antenna.
 21. The apparatus of claim 20, wherein the control circuit is configured to provide a signal at the transmit output, the signal having a particular wavelength when propagating in the dipolar gas; and wherein a diameter of the circular portion is based on the wavelength. 